Topics in Quantum Computers

Neil Shenvi

Helmut Bez, Tony Croft

Quantum Computation presents the mathematics of quantum computation. The purpose is to introduce the topic of quantum computing to students in computer science, physics and mathematics who have no prior knowledge of this field. The book is written in two parts. The primary mathematical topics required for an initial understanding of quantum computation are dealt with in Part I: sets, functions, complex numbers and other relevant mathematical structures from linear and abstract algebra. Topics are illustrated with examples focussing on the quantum computational aspects which will follow in more detail in Part II. Part II discusses quantum information, quantum measurement and quantum algorithms. These topics provide foundations upon which more advanced topics may be approached with confidence. Features A more accessible approach than most competitor texts, which move into advanced, research-level topics too quickly for today's students. Part I is comprehensive in providing all necessary mathematical underpinning, particularly for those who need more opportunity to develop their mathematical competence. More confident students may move directly to Part II and dip back into Part I as a reference. Ideal for use as an introductory text for courses in quantum computing. Fully worked examples illustrate the application of mathematical techniques. Exercises throughout develop concepts and enhance understanding. End-of-chapter exercises offer more practice in developing a secure foundation.

Wenbo Qiao, Peng Zhang, Jiaming Zhao +1 more

Quantum machine learning aims to leverage quantum computing to enhance the computing capabilities and storage efficiency of classical machine learning. Among them, quantum generative models, as a type of unsupervised machine learning, have been proven to learn distributions that are outside of classical machine learning reach. However, there is limited work on how to truly utilize and validate a possible quantum advantage in practical applications, especially in the field of natural language processing. This paper proposes the first Quantum Topic Model (QTM) based on variational quantum circuits to validate and showcase the possible advantages of quantum computing for generative models. QTM not only generates random samples like generative models but also exhibits fitting capabilities similar to neural networks. Finally, we conducted experiments on real datasets, and the results showed that QTM achieved a 46.9% reduction in model parameters while obtaining 10.4% higher topic coherence and 0.2% higher topic diversity with fewer iterations than neural topic models.

Dennis Willsch

Peter Young

This is the text for a one quarter or one semester undergraduate course on quantum computing that has been given at the University of California Santa Cruz. It is intended for students in the physical sciences who have already studied linear algebra (though a review of this topic is given in the course). No prior knowledge of quantum mechanics is required. The most important topics covered are Shor's algorithm and an introduction to quantum error correction. Most of the text is a build-up to these topics.

Daniel A. Sabol, Avery M. Leider, Lewis Westfall +1 more

Quantum computing will likely change our world as we know it today. In bringing together fields such as quantum mechanics, mathematics, and computer science in their construction and application, quantum computers hold a promise of tremendous increase in processing power when compared to present day technology. For an educator, teaching this topic requires that consideration be given to the fact that quantum computing is not only based on hard-to-teach aspects of physics, math, and computing, but that quantum computing itself is still in the early stages of its development. What is certain is that concepts such as Shor’s and Grover’s algorithms have already been developed specifically for use with quantum computing. Both algorithms are the beneficiaries of quantum properties such as superposition and entanglement which are at the core of the new technology. This paper is presented in a bottom up structure starting with the explanation of the basic component, the qubit, before moving to superposition and entanglement and ending with a lucid explanation of both of the algorithms. Due to the complex nature of the topic, teaching this subject requires that certain measures be taken to teach all students at all levels and have them feel comfortable within themselves about the topic. The course is meant for anyone who wants to learn quantum computing. It is furthermore recommended that those attending have a blank slate so we start with new students. We would like to see a variety of students taking and passing the course, with that in mind, the explanations of the topics are done without employing an excessive amount of math common to other courses in quantum computing. The recommended approach for teaching is through the use of videos and a curriculum which is broken down so topics are made more general and the discussion of that effort is the main focus